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公开(公告)号：US08806197B2
公开(公告)日：2014-08-12
申请号：US13478288
申请日：2012-05-23
申请人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
发明人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
IPC分类号： H04L29/06
CPC分类号： H04L9/3066 , G06F7/725 , H04L9/30 , H04L9/3252
摘要： Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.
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2.发明申请Trapdoor One-Way Functions on Elliptic Curves and Their Application to Shorter Signatures and Asymmetric Encryption 有权椭圆曲线上的Trapdoor单向函数及其对较短签名和不对称加密的应用公开(公告)号：US20120314855A1
公开(公告)日：2012-12-13
申请号：US13495307
申请日：2012-06-13
IPC分类号： H04L9/28
CPC分类号： H04L63/0823 , G06F21/64 , H04L9/3066 , H04L9/3252
摘要： A new trapdoor one-way function is provided. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points.
摘要翻译： 提供了一个新的陷门单向功能。 在一般意义上，使用一些二次代数整数z。 然后找到曲线E和在E上定义[z]的有理图。有理图[z]是陷门单向函数。 z的明智选择将确保可以有效地计算[z]，难以反转，[z]定义的[z]的确定是困难的，而z的知识允许反转[ z]在一组椭圆曲线点上。
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公开(公告)号：US20120230494A1
公开(公告)日：2012-09-13
申请号：US13478288
申请日：2012-05-23
申请人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
发明人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
IPC分类号： H04L9/08
CPC分类号： H04L9/3066 , G06F7/725 , H04L9/30 , H04L9/3252
摘要： Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.
摘要翻译： 通过将至少一个操作数布置成具有相对较小的比特长度来提供有限域中的组操作的组合的加速计算。 在椭圆曲线组中，代表点R的值对应于其他两个点uG和vG的和的验证是通过导出比特长度减小的整数w，z获得的，并且使得v = w / z。 然后，验证等式R = uG + vQ可以被计算为-zR +（uz mod n）G + wQ = 0，其中z和w为减少的比特长度。 这在数字签名验证中是有益的，其中可以实现增加的验证。
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公开(公告)号：US08204232B2
公开(公告)日：2012-06-19
申请号：US11333296
申请日：2006-01-18
申请人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
发明人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
IPC分类号： H04L9/08
CPC分类号： H04L9/3066 , G06F7/725 , H04L9/30 , H04L9/3252
摘要： Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.
摘要翻译： 通过将至少一个操作数布置成具有相对较小的比特长度来提供有限域中的组操作的组合的加速计算。 在椭圆曲线组中，代表点R的值对应于其他两个点uG和vG的和的验证是通过导出比特长度减小的整数w，z获得的，并且使得v = w / z。 然后，验证等式R = uG + vQ可以被计算为-zR +（uz mod n）G + wQ = 0，其中z和w为减少的比特长度。 这在数字签名验证中是有益的，其中可以实现增加的验证。
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5.发明申请TRAPDOOR ONE-WAY FUNCTIONS ON ELLIPTIC CURVES AND THEIR APPLICATION TO SHORTER SIGNATURES AND ASYMMETRIC ENCRYPTION 有权椭圆曲线上的TRAPDOOR单向函数及其应用于短信签名和不对称加密公开(公告)号：US20110060909A1
公开(公告)日：2011-03-10
申请号：US12945234
申请日：2010-11-12
CPC分类号： H04L63/0823 , G06F21/64 , H04L9/3066 , H04L9/3252
摘要： The present invention provides a new trapdoor one-way function. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points. Every rational map is a composition of a translation and an endomorphism. The most secure part of the rational map is the endomorphism as the translation is easy to invert. If the problem of inverting the endomorphism and thus [z] is as hard as the discrete logarithm problem in E, then the size of the cryptographic group can be smaller than the group used for RSA trapdoor one-way functions.
摘要翻译： 本发明提供了一种新的陷门单向功能。 在一般意义上，使用一些二次代数整数z。 然后找到曲线E和在E上定义[z]的有理图。有理图[z]是陷门单向函数。 z的明智选择将确保可以有效地计算[z]，难以反转，[z]定义的[z]的确定是困难的，而z的知识允许反转[ z]在一组椭圆曲线点上。 每一个合理的地图都是一个翻译和一个同化的组合。 理性地图中最安全的部分是翻译易翻译的同化。 如果反转内生的问题，因此[z]与E中的离散对数问题一样困难，则密码组的大小可以小于用于RSA陷门单向函数的组的大小。
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6.发明授权Control of ethylene on alkyl aluminum chain growth processes using calorimetry 失效使用量热法控制烷基铝链生长过程中的乙烯
公开(公告)号：US5518932A
公开(公告)日：1996-05-21
申请号：US79470
申请日：1993-06-21
申请人： Robert P. Gallant , Isaac L. Smith , Joseph B. Tedder, Jr. , Lloyd T. Crasto , George A. Daniels
发明人： Robert P. Gallant , Isaac L. Smith , Joseph B. Tedder, Jr. , Lloyd T. Crasto , George A. Daniels
CPC分类号： G01N25/4873 , C07C2/88 , Y10T436/21
摘要： The process of preparing higher aluminum alkyls by olefin chain growth on alkyl aluminum is improved by using on-line flow-through calorimetry to determine the aluminum concentration of a process stream, such as the aluminum alkyl feed stream, by reacting a sample portion of the process stream with a molar excess of alcohol and measuring the change in temperature. The aluminum concentration of the stream can then be adjusted as required to maintain it within a selected range.
摘要翻译： 通过使用在线流通量热法来确定工艺流如铝烷基进料流的铝浓度，通过使烷基铝的样品部分反应来改善在烷基铝上通过烯烃链生长制备高级烷基铝的方法 过程流与摩尔过量的醇并测量温度的变化。 然后可以根据需要调节流的铝浓度以将其保持在选定的范围内。
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公开(公告)号：US08634562B2
公开(公告)日：2014-01-21
申请号：US13618451
申请日：2012-09-14
IPC分类号： G06F21/00
CPC分类号： G06F21/00 , H04L9/0841
摘要： Improper re-use of a static Diffie-Hellman (DH) private key may leak information about the key. The leakage is prevented by a key derivation function (KDF), but standards do not agree on key derivation functions. The module for performing a DH private key operation must somehow support multiple different KDF standards. The present invention provides an intermediate approach that neither attempts to implement all possible KDF operations, nor provide unprotected access to the raw DH private key operation. Instead, the module performs parts of the KDF operation, as indicated by the application using the module. This saves the module from implementing the entire KDF for each KDF needed. Instead, the module implements only re-usable parts that are common to most KDFs. Furthermore, when new KDFs are required, the module may be able to support them if they built on the parts that the module has implemented.
摘要翻译： 静态Diffie-Hellman（DH）私钥的不正确使用可能会泄漏关键字的信息。 通过密钥导出功能（KDF）来防止泄漏，但是标准对密钥导出函数并不一致。 用于执行DH私钥操作的模块必须以某种方式支持多种不同的KDF标准。 本发明提供了一种中间方法，既不试图实现所有可能的KDF操作，也不提供对原始DH私钥操作的不受保护的访问。 相反，模块将执行KDF操作的部分，如使用该模块的应用程序所示。 这样可以节省模块实现所需的每个KDF的整个KDF。 相反，该模块只能实现大多数KDF常用的可重复使用的部件。 此外，当需要新的KDF时，如果模块构建在模块实现的部件上，则模块可能能够支持它们。
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公开(公告)号：US20130064367A1
公开(公告)日：2013-03-14
申请号：US13620206
申请日：2012-09-14
申请人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
发明人： Marinus Struik , Daniel R. Brown , Scott A. Vanstone , Robert P. Gallant , Adrian Antipa , Robert J. Lambert
CPC分类号： H04L9/3066 , G06F7/725 , H04L9/30 , H04L9/3252
摘要： Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.
摘要翻译： 通过将至少一个操作数布置成具有相对较小的比特长度来提供有限域中的组操作的组合的加速计算。 在椭圆曲线组中，代表点R的值对应于其他两个点uG和vG的和的验证是通过导出比特长度减小的整数w，z获得的，并且使得v = w / z。 然后，验证等式R = uG + vQ可以被计算为-zR +（uz mod n）G + wQ = 0，其中z和w为减少的比特长度。 这在数字签名验证中是有益的，其中可以实现增加的验证。
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9.发明授权Trapdoor one-way functions on elliptic curves and their application to shorter signatures and asymmetric encryption 有权椭圆曲线上的Trapdoor单向函数及其对较短签名和非对称加密的应用公开(公告)号：US07844051B2
公开(公告)日：2010-11-30
申请号：US11272152
申请日：2005-11-14
IPC分类号： H04L9/30
CPC分类号： H04L63/0823 , G06F21/64 , H04L9/3066 , H04L9/3252
摘要： The present invention provides a new trapdoor one-way function. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points. Every rational map is a composition of a translation and an endomorphism. The most secure part of the rational map is the endomorphism as the translation is easy to invert. If the problem of inverting the endomorphism and thus [z] is as hard as the discrete logarithm problem in E, then the size of the cryptographic group can be smaller than the group used for RSA trapdoor one-way functions.
摘要翻译： 本发明提供了一种新的陷门单向功能。 在一般意义上，使用一些二次代数整数z。 然后找到曲线E和在E上定义[z]的有理图。有理图[z]是陷门单向函数。 z的明智选择将确保可以有效地计算[z]，难以反转，[z]定义的[z]的确定是困难的，而z的知识允许反转[ z]在一组椭圆曲线点上。 每一个合理的地图都是一个翻译和一个同化的组合。 理性地图中最安全的部分是翻译易翻译的同化。 如果反转内生的问题，因此[z]与E中的离散对数问题一样困难，则密码组的大小可以小于用于RSA陷门单向函数的组的大小。
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公开(公告)号：US06430690B1
公开(公告)日：2002-08-06
申请号：US09628045
申请日：2000-07-28
IPC分类号： G06F124
CPC分类号： G07F7/1008 , G06Q20/341 , G06Q20/40975 , H04L9/3263 , H04L9/3271 , H04L9/3273
摘要： A protocol for authenticating at least one of a pair of first and second correspondents C and T in a data communication system, the method comprising the steps or storing a public key in the first correspondent C; computing a shared secret by the second correspondent T incorporating the public key C; storing the shared secret in the first correspondent C: the second correspondent T generating a challenge value a; the first correspondent C transmitting to the second correspondent T information including the stored public key C; the second correspondent T computing a test shared secret from the received public key C; the first and second correspondents computing response signals using the challenge value z and the shared secret in a one-way function fr; and the first correspondent C transmitting the computed response signal to the second correspondent T whereby the second correspondent verifies the first correspondent.
摘要翻译： 一种用于在数据通信系统中验证一对第一和第二通信对象C和T中的至少一个的协议，所述方法包括以下步骤或在第一对应C中存储公共密钥; 由包含公共密钥C的第二记者T计算共享秘密; 将共享秘密存储在第一通信对象C中：生成询问值a的第二通信对象T; 第一通讯员C发送到包括存储的公开密钥C的第二通讯员T信息; 第二通讯员T从所接收的公钥C计算测试共享秘密; 第一和第二记者使用挑战值z和单向函数fr中的共享秘密来计算响应信号; 并且第一通信对象C将计算出的响应信号发送到第二通信对象T，由此第二对方验证第一通信对方。
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